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Subjects
Class 10MathematicsSetsOperations on Sets (Union, Intersection, Difference)MediumLevel 17

If n(A) = 31, n(B) = 28, and n(A ∪ B) = 46, what is n(A ∩ B)?

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Answer and explanation

Correct answer: 13

Use the two-set formula n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substituting the values gives 46 = 31 + 28 − n(A ∩ B), so n(A ∩ B) = 31 + 28 − 46 = 13. The common elements must be subtracted from the sum because they were counted twice. Therefore option A is correct.

Tags

setscardinalityintersectioninclusion-exclusionOperations on Sets (UnionDifference)operations on sets union intersection differenceMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

13

Why is this the correct answer?

Use the two-set formula n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substituting the values gives 46 = 31 + 28 − n(A ∩ B), so n(A ∩ B) = 31 + 28 − 46 = 13. The common elements must be subtracted from the sum because they were counted twice. Therefore option A is correct.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).

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